Prikladnaya Mekhanika i Tekhnicheskaya Fizika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Prikl. Mekh. Tekh. Fiz.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2009, Volume 50, Issue 2, Pages 24–36 (Mi pmtf1713)  

This article is cited in 5 scientific papers (total in 5 papers)

Equations of the shallow water model on a rotating attracting sphere. 1. Derivation and general properties

A. A. Cherevkoab, A. P. Chupakhinab

a Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk, 630090, Russia
b Novosibirsk State University, Novosibirsk, 630090, Russia
Full-text PDF (340 kB) Citations (5)
Abstract: A shallow water model on a rotating attracting sphere is proposed to describe large-scale motions of the gas in planetary atmospheres and of the liquid in the world ocean. The equations of the model coincide with the equations of gas-dynamic of a polytropic gas in the case of spherical gas motions on the surface of a rotating sphere. The range of applicability of the model is discussed, and the conservation of potential vorticity along the trajectories is proved. The equations of stationary shallow water motions are presented in the form of Bernoulli and potential vorticity integrals, which relate the liquid depth to the stream function. The simplest stationary solutions that describe the equilibrium state differing from the spherically symmetric state and the zonal flows along the parallels are found. It is demonstrated that the stationary equations of the model admit the infinitely dimensional Lie group of equivalence.
Keywords: shallow water, motions on a sphere, Lie groups, potential vorticity, stationary solutions.
Received: 29.10.2007
Accepted: 04.04.2008
English version:
Journal of Applied Mechanics and Technical Physics, 2009, Volume 50, Issue 2, Pages 188–198
DOI: https://doi.org/10.1007/s10808-009-0026-x
Bibliographic databases:
Document Type: Article
UDC: 532.5+533+517.9
Language: Russian
Citation: A. A. Cherevko, A. P. Chupakhin, “Equations of the shallow water model on a rotating attracting sphere. 1. Derivation and general properties”, Prikl. Mekh. Tekh. Fiz., 50:2 (2009), 24–36; J. Appl. Mech. Tech. Phys., 50:2 (2009), 188–198
Citation in format AMSBIB
\Bibitem{CheChu09}
\by A.~A.~Cherevko, A.~P.~Chupakhin
\paper Equations of the shallow water model on a rotating attracting sphere. 1.~Derivation and general properties
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2009
\vol 50
\issue 2
\pages 24--36
\mathnet{http://mi.mathnet.ru/pmtf1713}
\elib{https://elibrary.ru/item.asp?id=11839325}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2009
\vol 50
\issue 2
\pages 188--198
\crossref{https://doi.org/10.1007/s10808-009-0026-x}
Linking options:
  • https://www.mathnet.ru/eng/pmtf1713
  • https://www.mathnet.ru/eng/pmtf/v50/i2/p24
    Cycle of papers
    This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Prikladnaya Mekhanika i Tekhnicheskaya Fizika Prikladnaya Mekhanika i Tekhnicheskaya Fizika
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024